Question

The diagram given below shows a ski jump. A skier weighing 60 kgf stands at A at the top of ski jump. He moves from A and takes off for his jump at B.

1. Calculate the change in the gravitational potential energy of the skier between A and B.
2. If 75% of the energy in part
   1. becomes kinetic energy at B.
   2. Calculate the speed at which the skier arrives at B. (Take g = 10 m s^-2)

Answer 1

Force = weight of skier = 60 kgf = (60 × 10) N

∴ Mass of skier m = 60 kg

Height at A, h₁ = 75 m; Height at B, h₂ = 15 m

(a) ∴ Change in Gravitational potential energy between A and B = mgh

= mgh₁ - mgh₂

= mg [h₁ - h₂]

= 60 × 10 [75 - 15]

= 600 × 60

= 36000 J 

= `36/10 xx 10000`

= 3.6 × 10⁴ J

(b) 75 % of changes in energy = `(36000 xx 75)/100`
= 27000 J

which becomes K.E

∴ K.E. at B = 27000 J

`1/2 mv^2 = 27000`

`1/2 xx 60  v^2 = 27000`

∴ `v^2 = 27000/30`

= 900 J

12 V = `sqrt900`

= 30 ms^-1